Well, in a Pie chart, you most likely would like to place the label in the middle.

where in the circle is no much of a problem:
so if your slice is from 0.1[rad] to 0.3[rad] then you should place it along the avarage radious (0.1[rad] + 0.3[rad])/2 = 0.2[rad] radius.

the tricky part is where along the radius:
your triangle is 'isosceles' so given height from it's TOP, the width between it's polygonals is easy to determine,tg(alpha/2) = (w/2) / hh = w/2 / tg(alpha / 2)

if h is larger than your PIE-Chart radius, you are placing the label outside the Chart, you should consider a constant R for that with a nice looking line.

cheers.

-- Edit 2 --
Note, there are two things to consider :

when your slice is larger than pi[rad] = 180 deg, the above calculation will fail, but in this situation the label should fit nicely.

you should specify at what minimum distance from the center along the radius you want your label, and if h comes lesser then, just use the minimum. (i'd say about 0.7r is a good value, but make it configurable.